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Un+l <1 = (x+2)** (n+1)2ª+I n2" (x+2) <1 = lim G4) <1 = <1 = |x+ 2| < 2 25. lim n 00 n- 00 > -2

Un+l <1 = (x+2)** (n+1)2ª+I n2" (x+2) <1 = lim G4) <1 = <1 = |x+ 2| < 2 25. lim n 00 n- 00 > -2

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.5: The Binomial Theorem
Problem 16E
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25. lim Untl <1 = (x+2)*+! (n+ 1)2=+1 n2 (x+ 2) lim () < 1 = <1 = |x +2| < 2 lim n- 00 <1 = n - 00 = -2 < x + 2 < 2 -4 <x < 0; when x = -4 we have , a divergent series; when x = 0 we have n n=1 the alternating harmonic series which converges conditionally n=1 (a) the radius is 2; the interval of convergence is -4 < x <0 (b) the interval of absolute convergence is -4 < x < 0 H.w 1 (c) the series converges conditionally at x = 0
Transcribed Image Text:25. lim Untl <1 = (x+2)*+! (n+ 1)2=+1 n2 (x+ 2) lim () < 1 = <1 = |x +2| < 2 lim n- 00 <1 = n - 00 = -2 < x + 2 < 2 -4 <x < 0; when x = -4 we have , a divergent series; when x = 0 we have n n=1 the alternating harmonic series which converges conditionally n=1 (a) the radius is 2; the interval of convergence is -4 < x <0 (b) the interval of absolute convergence is -4 < x < 0 H.w 1 (c) the series converges conditionally at x = 0
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